When comparing scaled coordinates between papers and code input scripts, always make sure that they use the same coordinate systems and definitions for a unit cell (both real and reciprocal space). For example while many sources (like the paper of Curtarolo, Setyawan) assume a 120° degree angle between $a$ and $b$ for a hexagonal cell, you can also define it to be a 60° angle (like the default in CP2K).

Once you have verified that your calculation setup works, use nohup mpirun -np 4 cp2k.popt … & again to run the calculations in parallel and in the background since they may take longer to complete than before.

Vacancy in graphene

Comparing energies

Use the provided template and its initial geometry to setup a single point energy calculation for a 6x6x1 supercell of graphene.

Create a vacancy by removing one carbon atom from this supercell and perform the energy calculation again.

Quick question: Does it matter which carbon atom you remove? (hint: what kind of boundary conditions do we impose?)

Calculate the energy of the vacancy formation, that is $E_v = E_2 - \frac{N-1}{N} \cdot E_1$ where $E_1$ is the energy of the complete system, $E_2$ that of the system with a vacancy and $N$ the number of atoms.

Analyze the PDOS

Would you expect the vacancy to haven any influence on the projected density of states? Check whether your assumption was right by visualizing the PDOS.

Replacement with oxygen

Now, instead of removing one carbon atom from the 6x6x1 supercell, simply replace it with an oxygen atom (remember: you have to a KIND section for oxygen). Perform first a single point calculation and second a geometry optimization (as shown in a previous exercise) and compare the energy of adsorption for both cases.